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- W2964686921 abstract "In this paper, we investigate the boundedness of a square function from ergodic theory on noncommutative $L_{p}$-spaces. The main result is a weak $(1,1)$ type estimate of this square function. We also show the $(L_{infty},mathrm{BMO})$ estimate, and thus strong $(L_{p},L_{p})$ estimate by interpolation. The main novel difficulty lies in the fact that the kernel of this square function does not enjoy any regularity, which is crucial in showing such endpoint estimates for standard noncommutative Calder'on-Zygmund singular integral operators." @default.
- W2964686921 created "2019-08-13" @default.
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- W2964686921 date "2019-07-31" @default.
- W2964686921 modified "2023-09-24" @default.
- W2964686921 title "Noncommutative weak $(1,1)$ type estimate for a square function from ergodic theory" @default.
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- W2964686921 doi "https://doi.org/10.48550/arxiv.1907.13499" @default.
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